If one defines “terrorism” as an attempt by a particular group to achieve a major long-term political change or goal, through acts of individual murder and sabotage, then one can find numerous instances of this kind of endeavor in the 20th century.
For example, there is the Serbian Black Hand Society, which for several years had a goal to create Greater Serbia, and to achieve that end brought about the assassination of the Austrian Archduke Franz Ferdinand on July 28, 1914, which ultimately led to the First World War. That is possibly the most significant act of terrorism in history. One could also cite the Irish Republican Army and its long struggle against Northern Ireland and England, the Mau Mau in Kenya, the Hukbalahop in the Philippines — all major terrorist movements of the last century. We ended the last century with the development of Islamic terrorism.